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Lack of compactness in the 2D critical Sobolev embedding, the general case

✍ Scribed by Hajer Bahouri; Mohamed Majdoub; Nader Masmoudi

Book ID
116389972
Publisher
Elsevier Science
Year
2012
Tongue
English
Weight
154 KB
Volume
350
Category
Article
ISSN
1631-073X

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✍ Stéphane Jaffard 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 128 KB

Let (u n ) be a bounded sequence in H s, p (R d ) (0<s<d p). We show that (u n ) has a subsequence (u$ n ) such that each u$ n can be expressed as a finite sum (plus a remainder) of translationsÂdilations of functions , m and such that the remainder has arbitrary small norm in L q (1Âq=(1Âp)&(sÂd )